Two different methodologies for geoid determination from ground and airborne gravity data

Abstract

S U M M A R YIn this study, two methodologies are investigated for geoid determination from ground and airborne gravity data. These two methodologies depend on the downward continuation method used. The first is the inverse Poisson integral; the second is the normal free-air gradient. Each of the two methods requires different treatment of the terrain effects and in turn different approaches to determine the geoid. The two geoid solutions, from ground data, are compared with existing GPS/levelling benchmarks and it is found that the second method gives a better fit due to the bias introduced from the inverse Poisson integral. The same process was applied to the airborne data, but with additional processing, that is the filtering of the terrain effects to preserve the consistency of the data due to the filtering of the airborne data. A study on the effect of filtering was also carried out in this paper and it concluded that filtering the terrain effects has no impact on the geoid. In addition, the airborne data, filtered to three different cut-off frequencies, were used to compute the geoid to investigate the possibility of using the denser data, of lower accuracy, to determine a high-resolution geoid. Even though the data filtered to small cut-off frequency have poorer agreement with the ground data, the geoids computed from the different filtered data is the nearly the same.The methodology of geoid determination from airborne data depends, among other things, on the procedure of downward continuing the gravity data. Downward continuation can be accomplished by either inverse Poisson integral (Heiskanen & Moritz 1967), free-air gradient (Heiskanen & Moritz 1967), collocation (Moritz 1980), or analytical downward continuation (Moritz 1980). Each of these methods necessitates different methodology in computing the gravity data at the reference sphere, and in turn the geoid determination. In this study, we analyse two methodologies that take into account the downward continuation done by, first, the inverse Poisson integral that will be named the first methodology and, second, by the use of the normal free-air gradient that will be named the second methodology. As for the terrain reduction procedure, the second Helmert condensation technique is followed in spherical approximation. In the second Helmert condensation technique, all masses above the geoid are condensed to an infinitely thin layer on the geoid.The main difference between these two methods is in the processing of the terrain effects, where the first methodology demands that the effects of the removed topographical masses and the condensed ones be evaluated at the measuring location. The second methodology requires that the effects of the removed topographical masses be evaluated at the measuring location and the condensed ones be evaluated at the reference sphere, i.e. at height zero. Two data types are used here, both located in the Canadian Rocky Mountains; the first is ground gravity anomalies, the second is airborne gravity disturbances.In addition t...

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